An inviscid fluid is bounded above by a horizontal plane and below by finite-amplitude ridges. The fluid is rotating and stratified. A uniform transport is forced across the ridges at small dynamical Rossby number, although the boundary conditions are such that motion cannot remain geostrophic. The most significant parameter is found to be a thermal Rossby number based upon the vertical density difference and both vertical and horizontal length scales, but independent of the transport. Conditions determining whether or not effects of the bottom topography will penetrate vertically throughout the fluid are discussed. Some numbers characteristic of flow in the deep ocean are presented.